Question: Simplify the following expression: $ y = \dfrac{-5}{4} + \dfrac{-7x - 6}{-2x + 6} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2x + 6}{-2x + 6}$ $ \dfrac{-5}{4} \times \dfrac{-2x + 6}{-2x + 6} = \dfrac{10x - 30}{-8x + 24} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-7x - 6}{-2x + 6} \times \dfrac{4}{4} = \dfrac{-28x - 24}{-8x + 24} $ Therefore $ y = \dfrac{10x - 30}{-8x + 24} + \dfrac{-28x - 24}{-8x + 24} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{10x - 30 - 28x - 24}{-8x + 24} $ $y = \dfrac{-18x - 54}{-8x + 24}$ Simplify the expression by dividing the numerator and denominator by -2: $y = \dfrac{9x + 27}{4x - 12}$